JEE Exam > JEE Questions > Ten different letters of an alphabet are give...
Start Learning for Free
Ten different letters of an alphabet are given. Words with five letters are formed from these given letters. Then the number of words which have at least one letter repeated is
- a)69760
- b)30240
- c)99784
- d)none of these
Correct answer is option 'A'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
Ten different letters of an alphabet are given. Words with five letter...
The total number of words that can be formed is 105 and number of these words in which no letters are repeated is 10P5.
Hence the required number
= 105 − 10P5
= 100000 − 10 × 9 × 8 × 7 × 6
= 69760
Hence the required number
= 105 − 10P5
= 100000 − 10 × 9 × 8 × 7 × 6
= 69760
Most Upvoted Answer
Ten different letters of an alphabet are given. Words with five letter...
Explanation:
Given Information:
- Total number of letters given = 10
- Words to be formed have 5 letters
Approach:
To find the number of words with at least one letter repeated, we can use the principle of inclusion-exclusion. We will first calculate the total number of 5-letter words that can be formed using the given 10 letters, and then subtract the number of words with no repeated letters, two repeated letters, three repeated letters, and four repeated letters.
Calculations:
- Total number of 5-letter words = 10P5 = 10! / (10-5)! = 10 x 9 x 8 x 7 x 6 = 30240
- Number of words with no repeated letters = 10 x 9 x 8 x 7 x 6 = 30240
- Number of words with exactly two repeated letters = 10C2 x 8 x 7 = 30240
- Number of words with exactly three repeated letters = 10C3 x 7 = 8400
- Number of words with exactly four repeated letters = 10C4 = 210
Now, using the principle of inclusion-exclusion:
Number of words with at least one letter repeated = Total - (No repeated letters + 2 repeated letters - 3 repeated letters + 4 repeated letters)
Number of words with at least one letter repeated = 30240 - (30240 - 30240 + 8400 - 210) = 69760
Therefore, the correct answer is option (a) 69760.
Given Information:
- Total number of letters given = 10
- Words to be formed have 5 letters
Approach:
To find the number of words with at least one letter repeated, we can use the principle of inclusion-exclusion. We will first calculate the total number of 5-letter words that can be formed using the given 10 letters, and then subtract the number of words with no repeated letters, two repeated letters, three repeated letters, and four repeated letters.
Calculations:
- Total number of 5-letter words = 10P5 = 10! / (10-5)! = 10 x 9 x 8 x 7 x 6 = 30240
- Number of words with no repeated letters = 10 x 9 x 8 x 7 x 6 = 30240
- Number of words with exactly two repeated letters = 10C2 x 8 x 7 = 30240
- Number of words with exactly three repeated letters = 10C3 x 7 = 8400
- Number of words with exactly four repeated letters = 10C4 = 210
Now, using the principle of inclusion-exclusion:
Number of words with at least one letter repeated = Total - (No repeated letters + 2 repeated letters - 3 repeated letters + 4 repeated letters)
Number of words with at least one letter repeated = 30240 - (30240 - 30240 + 8400 - 210) = 69760
Therefore, the correct answer is option (a) 69760.
Attention JEE Students!
To make sure you are not studying endlessly, EduRev has designed JEE study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in JEE.
|
Explore Courses for JEE exam
|
|
Similar JEE Doubts
Top Courses for JEEView all
Ten different letters of an alphabet are given. Words with five letters are formed from these given letters. Then the number of words which have at least one letter repeated isa)69760b)30240c)99784d)none of theseCorrect answer is option 'A'. Can you explain this answer?
Question Description
Ten different letters of an alphabet are given. Words with five letters are formed from these given letters. Then the number of words which have at least one letter repeated isa)69760b)30240c)99784d)none of theseCorrect answer is option 'A'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Ten different letters of an alphabet are given. Words with five letters are formed from these given letters. Then the number of words which have at least one letter repeated isa)69760b)30240c)99784d)none of theseCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Ten different letters of an alphabet are given. Words with five letters are formed from these given letters. Then the number of words which have at least one letter repeated isa)69760b)30240c)99784d)none of theseCorrect answer is option 'A'. Can you explain this answer?.
Ten different letters of an alphabet are given. Words with five letters are formed from these given letters. Then the number of words which have at least one letter repeated isa)69760b)30240c)99784d)none of theseCorrect answer is option 'A'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Ten different letters of an alphabet are given. Words with five letters are formed from these given letters. Then the number of words which have at least one letter repeated isa)69760b)30240c)99784d)none of theseCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Ten different letters of an alphabet are given. Words with five letters are formed from these given letters. Then the number of words which have at least one letter repeated isa)69760b)30240c)99784d)none of theseCorrect answer is option 'A'. Can you explain this answer?.
Solutions for Ten different letters of an alphabet are given. Words with five letters are formed from these given letters. Then the number of words which have at least one letter repeated isa)69760b)30240c)99784d)none of theseCorrect answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of Ten different letters of an alphabet are given. Words with five letters are formed from these given letters. Then the number of words which have at least one letter repeated isa)69760b)30240c)99784d)none of theseCorrect answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Ten different letters of an alphabet are given. Words with five letters are formed from these given letters. Then the number of words which have at least one letter repeated isa)69760b)30240c)99784d)none of theseCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for Ten different letters of an alphabet are given. Words with five letters are formed from these given letters. Then the number of words which have at least one letter repeated isa)69760b)30240c)99784d)none of theseCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of Ten different letters of an alphabet are given. Words with five letters are formed from these given letters. Then the number of words which have at least one letter repeated isa)69760b)30240c)99784d)none of theseCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Ten different letters of an alphabet are given. Words with five letters are formed from these given letters. Then the number of words which have at least one letter repeated isa)69760b)30240c)99784d)none of theseCorrect answer is option 'A'. Can you explain this answer? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup